In two triangles ABC and DEF , it is given that ∠ A = ∠ D , ∠ B = ∠ E and ∠ C = ∠ F . Are the two triangles necessarily congruent?

Question

In two triangles ABC and DEF , it is given that &#x2220; A = &#x2220; D , &#x2220; B = &#x2220; E and &#x2220; C = &#x2220; F . Are the two triangles necessarily congruent?

Philoid · Accepted Answer

No, the two triangles are not necessarily congruent in the given case as knowing only angle-angle-angle (AAA) does not work because it can produce similar but not congruent triangles.

In two triangles ABC and DEF, it is given that ∠A = ∠D, ∠B = ∠E and ∠C = ∠F. Are the two triangles necessarily congruent?